Planning and learning in permutation groups

Planning is defined as the problem of synthesizing a desired behavior from given basic operations, and learning is defined as the dual problem of analyzing a given behavior to determine the unknown basic operations. Algorithms for solving these problems in the context of invertible operations on finite-state environments are developed. In addition to their obvious artificial intelligence applications, the algorithms can efficiently find the shortest way to solve Rubik´s cube, test ping-pong protocols, and solve systems of equations over permutation groups